Question: 4 people can paint 6 walls in 47 minutes. How many minutes will it take for 6 people to paint 10 walls? Round to the nearest minute.
Answer: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 6\text{ walls}\\ p &= 4\text{ people}\\ t &= 47\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{6}{47 \cdot 4} = \dfrac{3}{94}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 10 walls with 6 people. $t = \dfrac{w}{r \cdot p} = \dfrac{10}{\dfrac{3}{94} \cdot 6} = \dfrac{10}{\dfrac{9}{47}} = \dfrac{470}{9}\text{ minutes}$ $= 52 \dfrac{2}{9}\text{ minutes}$ Round to the nearest minute: $t = 52\text{ minutes}$